Coexisting Hidden and self-excited attractors in an economic system of integer or fractional order

TL;DR

This paper investigates the complex dynamics of an economic system with foreign financing, revealing coexisting hidden and self-excited attractors in both integer and fractional order models, which could impact economic stability analysis.

Contribution

It introduces the coexistence of hidden and self-excited attractors in an economic system with integer and fractional order, highlighting their potential economic implications.

Findings

Multiple coexisting attractors identified in integer-order system.

Hidden attractors may influence economic stability due to foreign capital dynamics.

Fractional-order system exhibits unique attractor coexistence in fractional space.

Abstract

In this paper the dynamics of an economic system with foreign financing, of integer or fractional order, are analyzed. The symmetry of the system determines the existence of two pairs of coexisting attractors. The integer-order version of the system proves to have several combinations of coexisting hidden attractors with self-excited attractors. Because one of the system variables represents the foreign capital in ow, the presence of hidden attractors could be of a real interest in economic models. The fractional-order variant presents another interesting coexistence of attractors in the fractional order space.